During training stage, only the compression of the whole image is considered, following  [1]}, [2]}. Then the RDO problem in Equation REF  can further be formulated as following:
\(\begin{split}R +\lambda \cdot {D} =&\mathbb {E}_{x\sim {p_x}}[-{\log _{2}{p_{\hat{y}}{(\lfloor {f(x)}\rceil )}}}] \\+& \lambda \cdot \mathbb {E}_{x\sim {p_x}}[d(x,g(\lfloor {f(x)}\rceil ))],\end{split}\) 
